Problem: Simplify the following expression: $k = \dfrac{-3q^2 - 30q - 63}{q + 7} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-3$ , so we can rewrite the expression: $ k =\dfrac{-3(q^2 + 10q + 21)}{q + 7} $ Then we factor the remaining polynomial: $q^2 + {10}q + {21} $ ${7} + {3} = {10}$ ${7} \times {3} = {21}$ $ (q + {7}) (q + {3}) $ This gives us a factored expression: $\dfrac{-3(q + {7}) (q + {3})}{q + 7}$ We can divide the numerator and denominator by $(q - 7)$ on condition that $q \neq -7$ Therefore $k = -3(q + 3); q \neq -7$